advertisement

Name: Codename: Open book, calculators allowed. SHOW ALL OF YOUR WORKING. 1. [5 points ] Write the function ( ) = 2 2 + 12 , 14 in the form ( ) = ( , )2 + by completing the square. [Hint: multiply out your answer to check that it equals 2 2 + 12 , 14.] f x x x x f x a x h k x Solution: ( ) = 2 2 + 12 , 14 = 2 ( 2 + 6 , 7) = 2 ( 2 + 6 + 9 , 9 , 7) = 2 ( 2 + 6 + 9 , 16) = 2 ( + 3)2 , 32 f x x x x x x x x x x 1 point 1 point 1 point 2 points : 2. [2 points ] Find the zeros of the function ( ). 2 +12 , 14 = 2( +7)( , 1) = 0 so zeros are = ,7 1. Solution: Factor 2 One point for each correct zero. 3. [3 points ] Draw the graph of = 2 2 + 12 , 14. Identify the -intercept, the intercepts and the vertex. Solution: The -intercept is (0 ,14) (1 point), the -intercepts are (,7 0) and (1 0) (1 point for plotting both correctly), while the vertex is (,3 ,32) (1 point for plotting correctly). Join these dots with a smooth parabola. f x x x y y x x x x x ; ; y x x ; ; ; 1